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Simplifying 7x2 + -47x + 14 = 0 Reorder the terms: 14 + -47x + 7x2 = 0 Solving 14 + -47x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2 + -6.714285714x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6.714285714x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -6.714285714x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6.714285714x + x2 = 0 + -2 -6.714285714x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6.714285714x + x2 = -2 The x term is -6.714285714x. Take half its coefficient (-3.357142857). Square it (11.27040816) and add it to both sides. Add '11.27040816' to each side of the equation. -6.714285714x + 11.27040816 + x2 = -2 + 11.27040816 Reorder the terms: 11.27040816 + -6.714285714x + x2 = -2 + 11.27040816 Combine like terms: -2 + 11.27040816 = 9.27040816 11.27040816 + -6.714285714x + x2 = 9.27040816 Factor a perfect square on the left side: (x + -3.357142857)(x + -3.357142857) = 9.27040816 Calculate the square root of the right side: 3.044734497 Break this problem into two subproblems by setting (x + -3.357142857) equal to 3.044734497 and -3.044734497.Subproblem 1
x + -3.357142857 = 3.044734497 Simplifying x + -3.357142857 = 3.044734497 Reorder the terms: -3.357142857 + x = 3.044734497 Solving -3.357142857 + x = 3.044734497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.357142857' to each side of the equation. -3.357142857 + 3.357142857 + x = 3.044734497 + 3.357142857 Combine like terms: -3.357142857 + 3.357142857 = 0.000000000 0.000000000 + x = 3.044734497 + 3.357142857 x = 3.044734497 + 3.357142857 Combine like terms: 3.044734497 + 3.357142857 = 6.401877354 x = 6.401877354 Simplifying x = 6.401877354Subproblem 2
x + -3.357142857 = -3.044734497 Simplifying x + -3.357142857 = -3.044734497 Reorder the terms: -3.357142857 + x = -3.044734497 Solving -3.357142857 + x = -3.044734497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.357142857' to each side of the equation. -3.357142857 + 3.357142857 + x = -3.044734497 + 3.357142857 Combine like terms: -3.357142857 + 3.357142857 = 0.000000000 0.000000000 + x = -3.044734497 + 3.357142857 x = -3.044734497 + 3.357142857 Combine like terms: -3.044734497 + 3.357142857 = 0.31240836 x = 0.31240836 Simplifying x = 0.31240836Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.401877354, 0.31240836}
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